The invention is directed to a digital signal processor system, and more particularly to a system for processing one dimensional numerical data and multi-dimensional numerical data for solving speech and image processing problems, differential equation problems and the like, by transforming the data into a wavelet form for analysis and then synthesizing the original data, using modular elements to perform specific operations, including wavelet transforms, on input sequences and arrays of numerical data.
The text Multirate Digital Signal Processing, Crochiere et al, 1983 at pages 378-392 and references cited therein at pages 396-404 describe generic digital hardware realizations for implementing (i) a class of elementary digital signal processing operations known in the art of digital signal processing as quadrature mirror filters, and (ii) single side-band filter bank operations employing quadrature mirror filters.
The hardware realizations described in Crochiere et al consist of hardware components together with specific configurations of these components that are capable of performing single-side band quadrature mirror filter bank operations on input sequences of numerical data, herein called input signals. Filter bank operations consist of analysis operations that decompose input signals into constituent component signals and of synthesis operations that reconstruct the input signal from its constituent component signals. Filter bank operations have great utility in speech data compression and other digital signal processing applications. The hardware components described in Crochiere et al are described generically as low pass filters, high pass filters, downsamplers, and upsamplers. Specific designs for these component are not described in detail.
One useful type of analysis is performed using wavelet transforms. Mallat in a paper entitled "A Theory for Multiresolution Signal Decomposition: The Wavelet Representation", Department of Computer and Information Science, School of Engineering and Applied Science, University of Pennsylvania Report No. MS-CIS-87-22, GRASP LAB 103, May 1987 (hereinafter "Mallat 1", discusses a generic class of mathematical wavelet transforms and describes a pyramid architecture using quadrature mirror filters for efficiently calculating wavelet transforms. These pyramid architectures consist of:
(i) the single-side band quadrature mirror filter bank described in Crochiere et al for analyzing and for synthesizing one-dimensional signals, and
(ii) a pyramid architecture utilizing the same components as the architecture in (i) that are configured for computing two-dimensional wavelet transforms. The components described in Mallat 1 are described generically as low-pass filters, high-pass filters, downsamplers, and upsamplers. Specific designs for these components are not described in detail, and neither Crochiere et al or Mallat 1 describe configurations of hardware components for generation wavelet basis functions nor solving differential equations.
The use of wavelet theory and its associated transforms for performing useful digital signal processing and digital image processing is well established and specific applications in such fields as signal processing in seismic signal analysis, acoustics and speech compression and synthesis are discussed in Goupillaud et al, "Cycle-octave and Related Transforms in Seismic Signal Analysis", J. Math Phys., Vol. 26, p. 2473, 1985; Kronland-Martinet et al, "Analysis of Sounds Through Wavelet Transforms," Int'l J. Pattern Analysis and Artificial Intelligence, Vol 1, January 1987 (hereinafter "Kronland-Martinet") and Tuteur, "Wavelet Transformations in Signal Detection", Proc. 1988 Int'l Conf on Acoustics, Speech and Signal Processing, pp 1435-1438, 1988. It has been observed that the properties of wavelets are advantageous for (i) dealing with local properties of signals and images and (ii) for performing multiresolution analysis for signals and images. The importance of both of these tasks and the advantageous use of wavelets in this regard are generally acknowledged among those accomplished in the art. See, for example, Mallat 1; Mallat, Steven G., "Multiresolution Approximation and Wavelets," Department of Computer and Information Science, School of Engineering and Applied Science, University of Pennsylvania Report No. MS-CIS-87-87, GRASP LAB 80, September 1987 (hereinafter "Mallat 2"); Marr, Vision, H. Freeman & Co. 1982; and Pratt, Image Processing, J. Wiley & Sons, 1987.